Note 347 — Chapter III

Another method is to reduce Baroco and Bocardo by the process of ἔκθεσις to other moods of figures 2 and 3, and thence to figure 1. Ueberweg writes, “Baroco may also be referred to Camestres when those (some) S of which the minor premiss is true are placed under a special notion and denoted by Sʹ. Then the conclusion must hold good universally of Sʹ, and consequently particularly of S. Aristotle calls such a procedure ἔκθεσις” (Logic, § 113). As regards Bocardo, “Aristotle remarks that this mood may be proved without apagogical procedure (reductio ad impossibile) by the ἐκθέσθαι or λαμβάνειν of that part of the middle notion which is true of the major premiss. If we denote this part by N, then we get the premisses; NeP ; NaS: from which follows (in Felapton) SoP ; which was to be proved” (§ 115). The procedure is, however, rather more complicated than appears in the above statements. In the case of Baroco (PaM, SoM, ∴ SoP), let the S’s which are not M (of which by hypothesis there are some) be denoted by X ; then we have PaM, XeM, ∴ XeP (Camestres); but XaS, and hence we have further XeP, XaS, ∴ SoP (Felapton). In the case of Bocardo (MoP, MaS, ∴ SoP), let the M’s which are not P (of which by hypothesis there are some) be denoted by N ; then we have MaS, NaM, ∴ NaS (Barbara); and hence NeP, NaS, ∴ SoP (Felapton). The argument in both cases suggests questions connected with the existential import of propositions; but the consideration of such questions must for the present be deferred.